Given a [[Metric spaces]] $(X,d)$ we define the _topology of a metric space_, $\mathscr{O}(d)$ as the set of [open sets](open%20set), $X.$ Taken together $(X,\mathscr{O}(d))$ is a [topological vector space.](Topological%20vector%20spaces.md) #MathematicalFoundations/Geometry/Topology